# Proportional Usage of Low-Level Actions in Model Predictive Control for Six-Phase Electric Drives

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Six-Phase Electric Drive Generalities

## 3. PULLA-MPC Control Scheme

#### 3.1. Control Actions in PULLA-MPC

- Tangential $\alpha $-$\beta $ refinement: twelve LVVs can be selected to satisfy tangential requirements (Figure 3).
- Radial $\alpha $-$\beta $ refinement: the application time of the null voltage vector, ${V}_{null}$, adapts radial requirements as a function of the working conditions.

#### 3.2. PULLA-MPC Scheme

## 4. Results

#### 4.1. Test 1. Steady-State Performance of FPULLA-MPC and PULLA-MPC

#### 4.2. Test 2. Steady-State Performance of LVV-MPC and PULLA-MPC

#### 4.3. Test 3. Dynamic Performance of LVV-MPC and PULLA-MPC in a Speed-Ramp Scenario

#### 4.4. Test 4. Dynamic Performance of LVV-MPC and PULLA-MPC in a Load Torque Step

#### 4.5. Test 5. Dynamic Performance of LVV-MPC and PULLA-MPC in a Double Reversal-Speed Test

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Duran, M.J.; Levi, E.; Barrero, F. Multiphase Electric Drives: Introduction. In Wiley Encyclopedia of Electrical and Electronics Engineering; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 2017; pp. 1–26. [Google Scholar]
- Levi, E.; Jones, M.; Vukosavi, S.N.; Toliyat, H.A. A novel concept of a multiphase, multimotor vector controlled drive system supplied from a single voltage source inverter. IEEE Trans. Power Electron.
**2004**, 19, 320–335. [Google Scholar] [CrossRef] - Duran, M.J.; Gonzalez-Prieto, I.; Gonzalez-Prieto, A.; Barrero, F. Multiphase energy conversion systems connected to microgrids with inequal power-sharing capability. IEEE Trans. Energy Conv.
**2017**, 32, 1386–1395. [Google Scholar] [CrossRef] - Levi, E.; Bojoi, R.; Profumo, F.; Toliyat, H.A.; Williamson, S. Multiphase induction motor drives—A technology status review. IET Electric Power Appl.
**2007**, 1, 489–516. [Google Scholar] [CrossRef] [Green Version] - Gonçalves, P.F.C.; Cruz, S.M.A.; Mendes, A.M.S. Finite control set model predictive control of six-phase asymmetrical machines—An overview. Energies
**2019**, 12, 4693. [Google Scholar] [CrossRef] [Green Version] - Gonzalez-Prieto, I.; Zoric, I.; Duran, M.J.; Levi, E. Constrained model predictive control in nine-phase induction motor drives. IEEE Trans. Energy Conver.
**2019**, 34, 1881–1889. [Google Scholar] [CrossRef] - Luo, Y.; Liu, C. A flux constrained predictive control for a six-phase PMSM motor with lower complexity. IEEE Trans. Ind. Electron.
**2019**, 66, 5081–5093. [Google Scholar] [CrossRef] - Iqbal, A.; Alammari, R.; Mosa, M.; Abu-Rub, H. Finite set model predictive current control with reduced and constant common mode voltage for a five-phase voltage source inverter. In Proceedings of the IEEE 23rd International Symposium on Industrial Electronics (ISIE), Istanbul, Turkey, 1–4 June 2014; pp. 479–484. [Google Scholar]
- Gonzalez-Prieto, I.; Duran, M.J.; Aciego, J.J.; Martin, C.; Barrero, F. Model predictive control of six-phase induction motor drives using virtual voltage vectors. IEEE Trans. Ind. Electron.
**2018**, 65, 27–37. [Google Scholar] [CrossRef] - Garcia-Entrambasaguas, P.; Zoric, I.; Gonzalez-Prieto, I.; Duran, M.J.; Levi, E. Direct torque and predictive control strategies in nine-phase electric drives using virtual voltage vectors. IEEE Trans. Power Electron.
**2019**, 34, 12106–12119. [Google Scholar] [CrossRef] [Green Version] - Xue, C.; Song, W.; Wu, X.; Feng, X. Constant switching frequency finite-control-set predictive current control scheme of a five-phase inverter with duty-ratio optimization. IEEE Trans. Power Electron.
**2018**, 33, 3583–3594. [Google Scholar] [CrossRef] - Xue, C.; Song, W.; Feng, X. Finite control-set model predictive current control of five-phase permanent-magnet synchronous machine based on virtual voltage vectors. IET Electr. Power Appl.
**2017**, 11, 836–846. [Google Scholar] [CrossRef] - Luo, Y.; Liu, C. Multi-Vectors based model predictive torque control for a six-phase PMSM motor with fixed switching frequency. IEEE Trans. Energy Conv.
**2019**, 34, 1369–1379. [Google Scholar] [CrossRef] - Gonçalves, P.F.C.; Cruz, S.M.A.; Mendes, A.M.S. Fixed and variable amplitude virtual vectors for model predictive control of six-phase PMSMS with single neutral configuration. In Proceedings of the 2019 IEEE International Conference on Industrial Technology (ICIT), Melbourne, Australia, 13–15 February 2019; pp. 267–273. [Google Scholar]
- Luo, Y.; Liu, C. Elimination of harmonic currents using a reference voltage vector based-model predictive control for a six-phase PMSM motor. IEEE Trans. Power Electron.
**2019**, 34, 6960–6972. [Google Scholar] [CrossRef] - Aciego, J.J.; Gonzalez Prieto, I.; Duran, M.J. Model predictive control of six-phase induction motor drives using two virtual voltage vectors. IEEE J. Emerg. Sel. Top. Power Electron.
**2019**, 7, 321–330. [Google Scholar] [CrossRef] - Gonçalves, P.F.C.; Cruz, S.M.A.; Mendes, A.M.S. Predictive current control of six-phase permanent magnet synchronous machines with modulated virtual vectors. In Proceedings of the IECON 2019—45th Annual Conference of the IEEE Industrial Electronics Society, Lisbon, Portugal, 14–17 October 2019; pp. 6229–6234. [Google Scholar]
- Tatte, Y.N.; Aware, M.V. Torque ripple and harmonic current reduction in a three-level inverter fed direct-torque-controlled five-phase induction motor. IEEE Trans. Ind. Electron.
**2017**, 64, 5265–5275. [Google Scholar] [CrossRef] - Yu, B.; Song, W.; Tang, T.; Wang, S.; Bin, P.Y. A Finite control set model predictive current control scheme for five-phase PMSMS based on optimized duty ratio. In Proceedings of the 2019 IEEE Applied Power Electronics Conference and Exposition (APEC), Antheim, CA, USA, 17–21 March 2019. [Google Scholar]
- Duran, M.J.; Gonzalez-Prieto, I.; Gonzalez-Prieto, A. Large virtual voltaje vectors for direct controllers in six-phase electric drives. Int. J. Electron. Power Energy Syst.
**2021**, 125, 106425–106433. [Google Scholar] [CrossRef] - Aciego, J.J.; Gonzalez-Prieto, I.; Duran, M.J.; Bermudez, M.; Sales-Biedma, P. Model predictive control based on dynamic voltage vectors for six-phase induction machines. IEEE J. Emerg. Sel. Top. Power Electron.
**2020**. [Google Scholar] [CrossRef] - Gonzalez-Prieto, A.; Gonzalez-Prieto, I.; Duran, M.J. Smart voltage vectors for model predictive control of six-phase electric drives. IEEE Trans. Ind. Electron.
**2021**, 68, 9024–9035. [Google Scholar] [CrossRef] - Ayala, M.; Doval-Gandoy, J.; Rodas, J.; Gonzalez, O.; Gregor, R.; Rivera, M. A Novel Modulated Model Predictive Control Applied to Six-Phase Induction Motor Drives. IEEE Trans. Ind. Electron.
**2021**, 68, 3672–3682. [Google Scholar] [CrossRef] - Xheng, L.; Fletcher, J.E.; Williams, B.W.; He, X. A novel direct torque control scheme for a sensorless five-phase induction motor drive. IEEE Trans. Ind. Electron.
**2011**, 58, 503–513. [Google Scholar] - Pandit, J.K.; Aware, M.V.; Nemade, R.; Tatte, Y. Simplified implementation of synthetic vectors for DTC of asymmetric six-phase induction motor drives. IEEE Trans. Ind. Appl.
**2018**, 54, 2306–2318. [Google Scholar] [CrossRef] - Ren, Y.; Zhu, Z.Q. Reduction of both harmonic current and torque ripple for dual three-phase permanent-magnet synchronous machine using modified switching-table-based direct torque control. IEEE Trans. Ind. Electron.
**2015**, 62, 6671–6681. [Google Scholar] [CrossRef] - Che, H.S.; Levi, E.; Jones, M.; Hew, W.P.; Rahim, N.A. Current control methods for an asymmetrical six-phase induction motor drive. IEEE Trans. Power Electron.
**2014**, 29, 407–417. [Google Scholar] [CrossRef] [Green Version] - Zhao., Y.; Lipo, T.A. Space vector PWM control of dual three-phase induction machine using vector space decomposition. IEEE Trans. Ind. Appl.
**1995**, 31, 1100–1109. [Google Scholar] [CrossRef] - Gonzalez-Prieto, I.; Duran, M.J.; Barrero, F.; Bermudez, M.; Guzman, H. Impact of postfault flux adaptation on six-phase induction motor drives with parallel converters. IEEE Trans. Power Electron.
**2017**, 32, 515–528. [Google Scholar] [CrossRef] [Green Version] - Yepes, A.G.; Riveros, J.A.; Doval-Gandoy, J.; Barrero, F.; Óscar, L.; Bogado, B.; Jones, M.; Levi, E. Parameter identification of multiphase induction machines with distributed windings-part 1: Sinusoidal excitation methods. IEEE Trans. Energy Conv.
**2012**, 27, 1056–1066. [Google Scholar] [CrossRef] - Riveros, J.A. Parameter identification of multiphase induction machines with distributed windings-part 2: Time-domain techniques. IEEE Trans. Energy Conv.
**2012**, 27, 1067–1077. [Google Scholar] [CrossRef] - Hossein, H.; Faranda, R. A New Approach for Power Losses Evaluation of IGBT/Diode Module. Electronics
**2021**, 10, 280. [Google Scholar] - Nicolai, U.; Wintrich, A. Application Note AN 1403, Determining Switching Losses of SEMIKRON IGBT Modules. SEMIKRON International GmbH. 2014. Available online: https://www.semikron.com/service-support/downloads/detail/semikron-application-note-determining-switching-losses-of-semikron-igbt-modules-en-2014-08-19-rev-00.html (accessed on 12 July 2021).
- Datasheet IGBT SK30GB128 Modules. SEMIKRON International GmbH. 2006. Available online: https://datasheetspdf.com/pdf-file/831859/SemikronInternational/SK30GAL128/1 (accessed on 12 July 2021).

**Figure 2.**Voltage vectors in $\alpha $-$\beta $ and $x$-$y$ subspaces for an asymmetrical six-phase induction machine fed by a dual three-phase VSC.

**Figure 4.**Switching transition: (

**a**) Arbitrary null voltage vector selection and (

**b**) using an optimal null voltage vector selection.

**Figure 7.**Test 1. Steady-state performance of FPULLA-MPC (left) and PULLA-MPC (right). From top to bottom: (

**a**) motor speed, (

**b**) $d$-$q$ currents, (

**c**) $x$-$y$ currents, (

**d**) zoom of the $x$-$y$ currents, and (

**e**) set 1 of phase currents.

**Figure 8.**Test 2. Steady-state performance of LVV-MPC (left) and PULLA-MPC (right). From top to bottom: (

**a**) motor speed, (

**b**) $d$-$q$ currents, (

**c**) $x$-$y$ currents, (

**d**) zoom of the $x$-$y$ currents and (

**e**) set 1 of phase currents.

**Figure 9.**Test 3. Dynamic performance of LVV-MPC (left plots) and PULLA-MPC (right plots). From top to bottom: (

**a**) motor speed, (

**b**) $d$-$q$ currents, (

**c**) $x$-$y$ currents and (

**d**) application time of active voltage vectors.

**Figure 10.**Load torque step test for LVV-MPC (left plots) and PULLA-MPC (right plots). From top to bottom: (

**a**) motor speed, (

**b**) $d$-$q$ currents, (

**c**) $x$-$y$ currents and (

**d**) set 1 of phase currents.

**Figure 11.**Double reversal-speed test for PULLA-MPC. From top to bottom: (

**a**) motor speed, (

**b**) $d$-$q$ currents, (

**c**) $x$-$y$ currents, (

**d**) zoom 1 of set 1 of phase currents and (

**e**) zoom 2 of set 1 of phase currents.

Power | $1\mathrm{kw}$ |

Maximum $q$-current (${{i}_{q}|}_{max}$) | 4.5 A |

Stator Resistance (${R}_{s}$) | $14.2\mathsf{\Omega}$ |

Rotor Resistance (${R}_{r}$) | $3\mathsf{\Omega}$ |

Mutual Inductance (${L}_{m}$) | $420\mathrm{mH}$ |

Stator Leakage Inductance (${L}_{ls}$) | $3.5\mathrm{mH}$ |

Rotor Leakage Inductance (${L}_{lr}$) | $55\mathrm{mH}$ |

DC-Link Voltage (${V}_{DC}$) | $300\mathrm{V}$ |

Control Method | THD | ${\mathit{f}}_{\mathit{s}\mathit{w}\mathit{i}\mathit{t}\mathit{c}\mathit{h}\mathit{i}\mathit{n}\mathit{g}}$ |
---|---|---|

PULLA-MPC | 11.61% | 4.96 kHz |

FPULLA | 12.65% | 5.70 kHz |

Control Method | THD | ${\mathit{I}}_{\mathit{x}}{}_{\mathit{p}-\mathit{p}}$ | ${\mathit{f}}_{\mathit{s}\mathit{w}\mathit{i}\mathit{t}\mathit{c}\mathit{h}\mathit{i}\mathit{n}\mathit{g}}$ | ${\overline{\mathit{r}\mathit{m}\mathit{s}}}_{\mathit{p}\mathit{h}}^{2}$ |
---|---|---|---|---|

PULLA-MPC | 10.94% | 1.79 $\mathrm{A}$ | 4.9 kHz | 3.219 ${\mathrm{A}}^{2}$ |

LVV-MPC | 19.85% | 2.66 $\mathrm{A}$ | 3.4 kHz | 3.375 ${\mathrm{A}}^{2}$ |

Losses | LVV-MPC | PULLA-MPC |
---|---|---|

Stator copper losses (W) | 285.32 | 269.94 |

VSC switching losses (W) | 7.92 | 11.07 |

Total (W) | 293.24 | 281.01 |

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**MDPI and ACS Style**

Gonzalez-Prieto, A.; Gonzalez-Prieto, I.; Duran, M.J.; Carrillo-Rios, J.; Aciego, J.J.; Salas-Biedma, P.
Proportional Usage of Low-Level Actions in Model Predictive Control for Six-Phase Electric Drives. *Energies* **2021**, *14*, 4358.
https://doi.org/10.3390/en14144358

**AMA Style**

Gonzalez-Prieto A, Gonzalez-Prieto I, Duran MJ, Carrillo-Rios J, Aciego JJ, Salas-Biedma P.
Proportional Usage of Low-Level Actions in Model Predictive Control for Six-Phase Electric Drives. *Energies*. 2021; 14(14):4358.
https://doi.org/10.3390/en14144358

**Chicago/Turabian Style**

Gonzalez-Prieto, Angel, Ignacio Gonzalez-Prieto, Mario J. Duran, Juan Carrillo-Rios, Juan J. Aciego, and Pedro Salas-Biedma.
2021. "Proportional Usage of Low-Level Actions in Model Predictive Control for Six-Phase Electric Drives" *Energies* 14, no. 14: 4358.
https://doi.org/10.3390/en14144358